Coupled flexural-torsional nonlinear vibrations of microcantilever beams

S. Nima Mahmoodi; Nader Jalili

doi:10.1117/12.715821

11 April 2007 Coupled flexural-torsional nonlinear vibrations of microcantilever beams

S. Nima Mahmoodi, Nader Jalili

Proceedings Volume 6528, Nanosensors, Microsensors, and Biosensors and Systems 2007; 65281A (2007) https://doi.org/10.1117/12.715821
Event: SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, 2007, San Diego, California, United States

Abstract

In this paper the problem of coupled flexural-torsional nonlinear vibrations of a piezoelectrically-actuated microcantilever beam is investigated considering beam's simultaneous flexural, torsional and longitudinal vibrations. Application of such problem is utilized in several nanotechnological instruments such as atomic force microscopy, nanomechanical cantilever sensors and friction force microscopy. The actuation and sensing are both facilitated through bonding a piezoelectric layer (here, ZnO) on the microcantilever surface. The piezoelectric properties combined with nonlinear geometry of the beam introduce both linear and nonlinear coupling between flexural vibration as well as longitudinal and torsional vibrations. The governing equations of motion are obtained with piezoelectric nonlinearity appearing in quadratic form while inertia and stiffness nonlinearities as cubic. An experimental setup consisting of a commercial piezoelectric microcantilever installed on the stand of an ultramodern laser-based microsystem analyzer is designed and utilized to verify the theoretical developments. First and second flexural natural frequencies are both experimentally and numerically obtained and are shown to be in good agreement. Both linear and nonlinear simulation results are compared with experimental results and it is observed that nonlinear modeling response matches the experimental findings very closely.

Citation Download Citation

S. Nima Mahmoodi and Nader Jalili "Coupled flexural-torsional nonlinear vibrations of microcantilever beams", Proc. SPIE 6528, Nanosensors, Microsensors, and Biosensors and Systems 2007, 65281A (11 April 2007); https://doi.org/10.1117/12.715821

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available